Mathematics – Statistics Theory
Scientific paper
2008-06-10
Electron. J. Statist. 4 (2010), 334-360
Mathematics
Statistics Theory
second revision: new title, some comments added, proofs moved to appendix
Scientific paper
10.1214/09-EJS523
Confidence intervals based on penalized maximum likelihood estimators such as the LASSO, adaptive LASSO, and hard-thresholding are analyzed. In the known-variance case, the finite-sample coverage properties of such intervals are determined and it is shown that symmetric intervals are the shortest. The length of the shortest intervals based on the hard-thresholding estimator is larger than the length of the shortest interval based on the adaptive LASSO, which is larger than the length of the shortest interval based on the LASSO, which in turn is larger than the standard interval based on the maximum likelihood estimator. In the case where the penalized estimators are tuned to possess the `sparsity property', the intervals based on these estimators are larger than the standard interval by an order of magnitude. Furthermore, a simple asymptotic confidence interval construction in the `sparse' case, that also applies to the smoothly clipped absolute deviation estimator, is discussed. The results for the known-variance case are shown to carry over to the unknown-variance case in an appropriate asymptotic sense.
Pötscher Benedikt M.
Schneider Ulrike
No associations
LandOfFree
Confidence Sets Based on Penalized Maximum Likelihood Estimators in Gaussian Regression does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Confidence Sets Based on Penalized Maximum Likelihood Estimators in Gaussian Regression, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Confidence Sets Based on Penalized Maximum Likelihood Estimators in Gaussian Regression will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-175051